Beam Voltage Threshold for Excitation of Compressional

Alfvén Modes

E D Fredrickson,

J Menard, N Gorelenkov, S Kubota*, D Smith

Princeton Plasma Physics Laboratory

*University of California

Goal: Improved understanding of CAE instability

• Fast ion instabilities have potential to impact ignition threshold in fusion reactors.

• ST's, with intrinsic low field, are particularly susceptible to fast ion driven instabilities.

• This experiment documents which fast ions drive mode, necessary for benchmarking theoretical models.

• Sharp threshold in beam energy, but not in Vbeam/VAlfvén, is found.

Amplitude, number of modes, strong function of voltage above threshold.

• More CAE with higher voltage.

• Change in beam velocity only 6% from 70-80kV.

• Beam power weak factor.

60 ms 60 ms 60 ms 60 ms

90 kV 80 kV 70 kV 60 kV

2.5

2.0

1.5

1.0

0.5

0.0

Fre

quen

cy (

MH

z)

ci cicici

t

• Btor varied from 3 - 6 kG, small change in threshold;– Vbeam ≈ 2.1 - 2.4 x 106 m/s.

– Vbeamthr VAlfvén

(1/9)

• Drive is doppler-shifted cyclotron resonance: = l C - k Vdrift - kVBeam

(k Vdrift << kVBeam

• Most change in VAlfvén from Btor; could be beam.

• Only fast ions, above ≈ 50 keV, drive waves.

CAE have sharp beam voltage threshold, weak VAlfvén dependence

VAlfvén (106 m/s)

VB

eam

(10

6 m

/s)

45

50

55

60

65

Bea

m V

olta

ge (

kV)

“Stable”

“Unstable”

Threshold VA(1/9)

0.0 0.5 1.0 1.5 2.02.0

2.6

2.5

2.4

2.3

2.2

2.1

• Mode frequency predicted from simplified dispersion:

≈ k VAlfvén

and resonance condition: ≈ C - k Vdrift- k||Vb||

• k|| is adjustable, but range is reasonable.

• Mode frequencies are typically ≈ (0.5 - 0.6) ci.

Mode frequency consistent with resonance condition, dispersion.

“Predicted” frequency (MHz)

Mea

sure

d fr

eque

ncy

(MH

z)

0.0 0.5 1.0 1.5 2.0 2.50.0

0.5

1.0

1.5

2.0

2.5

Fraction of fast ion population available to drive mode is small

• Fast ions which can drive CAE must satisfy 1 < kb < 2 =>

1<(/ci)(vb/VA)<2

• Resonance condition means ions must be above ≈ 0.5-0.6 ci curve.

• Small fraction of fast ions drive mode.

80

60

40

20

0

V||/V

Ebe

am (

keV

)

-1.0 0.0 1.00.5-0.5

108841a02

0.6 ci

0.5 ci

Beam Injection energy

At higher field, essentially no fast ions available to drive mode.

• Fast ion population sensitive to density profile, temperature, etc.

• Threshold change primarily from increase in VAlfvén.

• More perpendicular fast ions destabilizing.

• "Bump-on-tail" in perp direction also req'd.

0.7 ci

80

60

40

20

0

V||/V

Eb

ea

m (

keV

)

-1.0 0.0 1.00.5-0.5

108842a02

Beam Injection Voltage

Summary

• Theoretical advances are finding qualitative and quantitative agreement with experimental determinations of CAE stability boundaries.

• Presently, the CAE appear to be relatively weakly driven modes with access to only a small fraction of beam injection power.

• Consistent with measured low growth rates.

• Fusion- population may or may not more effectively drive CAE.

• GAE's also believed observed…N Gorelenkov, Tuesday afternoon, poster session IV

Model of Compressional Alfvén waves

• Simple "harmonic oscillator" model can be derived from dispersion relation: d2/dr2 = m2 / r2 - 2 / VAlfvén

2.• De-stabilized by "bump-on-tail" with resonance

condition – l C – k Vdrift - kVBeam = 0, (l = 0,1)• Frequency:

minor radius

(/VAlfvén)2

(m/r)2

2 m2vA

2

k2r 2 1k||

2 2r2

m 2

1

1 i

i

2

r02 2s1

V||

V

Beam Slowing Down

Bump-on-tail

Neutron decay rate shows no strong anomaly

• Strong stochastic coupling of fast ions to CAE to thermal ions should affect fast ion population, neutron rate, decay rate.

• TRANSP calculation, recalibrated Thomson Te.

0.40.0 0.1 0.2 0.3

4.0

0.0

2.0

Neutron Source Rate(1013/s)

Time (sec)

106242a26 t106242.neu

Neutron rate TRANSP calc.

80 kV 70 kV 56 kV